Nonlinear sensitivity analysis of multiparameter model systems

Abstract

Large sets of coupled, nonlinear equations arise in a number of disciplines in connection with computer-based models of physical, social, and economic processes. Solutions for such large systems of equations must be effected by means of digital computers using appropriately designed codes. This paper addresses itself to the critically important problem of how sensitive the solutions are to variations of, or inherent uncertainties in, the parameters of the equation set. We review here, and also present further developments of, our statistical method of sensitivity analysis. The sensitivity analysis presented here is nonlinear and thus permits one to study the effects of large deviations from the nominal parameter values. In addition, since all parameters are varied simultaneously, one can explore regions of parameter space where several parameters deviate simultaneously from their nominal values. We develop here the theory of our method of sensitivity analysis, then detail the method of implementation, and finally present examples of its use.